Numerical simulation of friction stir welding by natural element methods

In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods (FEM) encounter several difficulties. While Lagrangian simulations suffer from mesh distortion, Eulerian or Arbitrary Lagrangian Eulerian (ALE) ones still have difficulties due to the treatment of convective terms, the treatment of the advancing pin, and many others. Meshless methods somewhat alleviate these problems, allowing for an updated Lagrangian framework in the simulation. Accuracy is not affected by mesh distortion (and hence the name meshless), but the price to pay is the computational cost, higher than in the FEM. The method used here, the Natural Element Method (NEM), presents some interesting characteristics, such as the ease of imposition of essential boundary conditions and coupling with FEM codes. Even more, since the method is formulated in a Lagrangian setting, it is possible to track the evolution of any material point during the process and also to simulate the Friction Stir Welding (FSW) of two slabs of different materials. The examples shown in this paper cover some of the difficulties related with the simulation of the FSW process: very large deformations, complex nonlinear and strongly coupled thermomechanical behaviour of the material and mixing of different materials.